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Rational \(S^{1}\)-Equivariant Stable Homotopy Theory

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J. P. C. Greenlees

The memoir presents a systematic study of rational
\(S^1\)-equivariant cohomology theories, and a complete algebraic model
for them. It provides a classification of such cohomology theories in
simple algebraic terms and a practical means of calculation. The power
of the model is illustrated by analysis of the Segal conjecture, the
behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of
\(S^1\)-equivariant \(K\)-theory, and the rational behaviour of cyclotomic
spectra and the topological cyclic homology construction.

Readership

Graduate students and research mathematicians working
in algebraic topology.

The memoir presents a systematic study of rational
\(S^1\)-equivariant cohomology theories, and a complete algebraic model
for them. It provides a classification of such cohomology theories in
simple algebraic terms and a practical means of calculation. The power
of the model is illustrated by analysis of the Segal conjecture, the
behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of
\(S^1\)-equivariant \(K\)-theory, and the rational behaviour of cyclotomic
spectra and the topological cyclic homology construction.